Work

Strong NP-Hardness for Sparse Optimization with Concave Penalty Functions

Year: 2015

Type: preprint

Abstract: Consider the regularized sparse minimization problem, which involves empirical sums of loss functions for $n$ data points (each of dimension $d$) and a nonconvex sparsity penalty. We prove that finding an $\mathcal{O}(n^{c_1}d^{c_2})$-optimal solution to the regularized sparse optimization problem is strongly NP-hard for any $c_1, c_2\in [0,1)$ such that $c_1+c_2<1$. The result applies to a broad class of loss functions and sparse penalty functions. It suggests that one cannot even approximately solve the sparse optimization problem in polynomial time, unless P $=$ NP.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1501.00622

Authors: Chen, Yichen, Ge, Dongdong, Wang, Mengdi, Wang, Zizhuo, Ye, Yinyu, Yin, Hao

Institutions: Princeton University, Shanghai University of Finance and Economics, University of Minnesota, Stanford University

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2641921428

Cites: 25

Cited by: 12

Related to: 10